1. Technical Field
The present invention relates to a system, a method and a computer readable medium for encoding a curve. In particular, this invention relates to a computer readable medium storing encoding programs which encode the conformations, i.e., spacial patterns, of curves.
2. Related Art
The function of a protein is determined by the three-dimensional structure of the protein. Thus, once three-dimensional structures are represented in a simple way, one could compare structural similarity of proteins using the data, instead of the complicated three-dimensional structures.
As a representation method of the shapes of three-dimensional objects, there are two known ways: one approximates the shape of an object using a combination of predetermined primitive objects (such as cuboids, spheres, and cylinders), the other uses polygon-meshes to approximate the surface of an object. As an example of approximation by primitive objects, WO02/101598 and WO03/040968 propose an encoding method of the conformations of curves in (N−1)-dimensional Euclidean space, where curves are approximated by a sequence of N-face polyhedrons and the conformation of a curve is described as a binary sequence (N denotes any natural number greater than 1).
As for mathematical representations of the backbone conformations of biopolymer molecules such as proteins, there are three known methods: C. Branden and J. Tooze, “Introduction to Protein Structure,” Garland Publishing Inc, New York (USA), 1998, pp. 9-10 explains the Ramachandran plot method, where the two backbone dihedral angles (the angle of rotation around the N—Ca bond and the angle around the C′—Ca bond from the same Ca atom) are plotted against each other in a two-dimensional diagram to characterize protein structures such as alpha-helices and beta-sheets. S. Rackovsky, H. A. Scheranga, “Differential Geometry and Polymer Conformation. 1.,” Macromolecules, 1978, 1168-1174 proposed a differential geometrical method, where protein backbones are approximated by a broken line to quantify the structural similarity of different proteins. P. Rogen, B. Fain, “Automatic classification of protein structure by using Gauss integrals,” Proc. Natl. Acad. Sci., 2003, 100, 119-124 proposed a topological method, where protein structures are described using 30 geometrical parameters for the purpose of classification.
Finally, WO03/040968 proposed an encoding method of three-dimensional biopolymer molecule structures (such as protein structures), where a biopolymer is approximated by a sequence of tetrahedrons and its conformation is represented by a binary sequence. Since the method makes it possible to describe the three-dimensional structures of biopolymers as one-dimensional number sequences, one could compute structural similarity of different polymers simply by comparing the corresponding number sequences.